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arXiv 0811.2178cond-mat.stat-mech
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薄膜中的Kosterlitz-无相变:三维晶格模型的Monte Carlo研究

Kosterlitz-Thouless transition in thin films: A Monte Carlo study of three-dimensional lattice models

Martin Hasenbusch

摘要:

我们在三维XY普适类中研究了薄膜的相变。为此,我们在简单立方晶格上对改进的双组分XY模型、改进的动态稀释XY模型和标准XY模型进行了Monte Carlo研究。我们研究的薄膜厚度L_0=32晶格间距。在晶格的短方向上采用自由边界条件。使用最近提出的有限尺寸标度(FSS)方法,我们确定了高精度的转变温度。Binder累积量U_4的有效二维有限尺寸标度行为、二阶矩相关长度随晶格尺寸的变化、反周期和周期边界条件下的配分函数的比值Z_a/Z_p以及螺旋度模量的变化都清楚地证实了该相变的无Kosterlitz性质。分析了相变温度随膜厚L_0的变化规律。证实了重整化群理论的预言。我们计算了在三维热力学极限下,在厚度为L_0的薄膜的Kosterlitz-无相变温度下,薄膜厚度L_0与横向关联长度λ_T的普适比:[ L_{0,KT} /λ_T]^* = 1.595(7)。这一结果可以与在λ-跃迁附近的~ 4 He薄膜上的实验结果相比较。

英文摘要:

We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component ϕ^4 model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L_0=32 lattice spacings. In the short direction of the lattice free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U_4, the second moment correlation length over the lattice size ξ_{2nd}/L, the ratio of the partition functions with anti-periodic and periodic boundary conditions Z_a/Z_p and the helicity modulus Υclearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L_0 of the film. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L_0 and the transversal correlation length ξ_T in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L_0: [L_{0,KT}/ξ_T]^* = 1.595(7). This results can be compared with experimental results on thin films of 4He near the λ-transition.

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